论文标题
通用信息组件分析
Common Information Components Analysis
论文作者
论文摘要
我们通过（放松）Wyner的共同信息对规范相关分析（CCA）进行信息理论解释。 CCA允许从两个高维数据集中提取低维描述（功能），这些描述使用相关性和线性变换的框架来捕获数据集之间的共同点。我们的解释首先将通用信息提取到预选的分辨率级别，然后将其投射回每个数据集。在高斯统计的情况下，此过程完全减少为CCA，分辨率级别指定提取的CCA组件的数量。这也表明了一种新型算法，通用信息组件分析（CICA），具有几个理想的特征，包括自然扩展到仅两个数据集。
We give an information-theoretic interpretation of Canonical Correlation Analysis (CCA) via (relaxed) Wyner's common information. CCA permits to extract from two high-dimensional data sets low-dimensional descriptions (features) that capture the commonalities between the data sets, using a framework of correlations and linear transforms. Our interpretation first extracts the common information up to a pre-selected resolution level, and then projects this back onto each of the data sets. In the case of Gaussian statistics, this procedure precisely reduces to CCA, where the resolution level specifies the number of CCA components that are extracted. This also suggests a novel algorithm, Common Information Components Analysis (CICA), with several desirable features, including a natural extension to beyond just two data sets.
